Now that the assumption of an infinite set of events has been made explicit, I don’t think it’s a problem. I think that other subtle violations of the axioms might be a problem, e.g. likelihoods not always comparable, etc would be more of a problem.
I’d like to see an example of a nonbayesian probability function in a finite world btw.
OK, fair enough, I guess the value of this paper was making that assumption explicit. Halpern’s 1999 paper (Perplexed links) constructs such an example.
Now that the assumption of an infinite set of events has been made explicit, I don’t think it’s a problem. I think that other subtle violations of the axioms might be a problem, e.g. likelihoods not always comparable, etc would be more of a problem.
I’d like to see an example of a nonbayesian probability function in a finite world btw.
OK, fair enough, I guess the value of this paper was making that assumption explicit. Halpern’s 1999 paper (Perplexed links) constructs such an example.
And is it in any way interesting? Does it allow you to do great inference beyond the ken of Bayesianism? Or is it just some annoying corner-case?
I haven’t spent time understanding the example, but Perplexed’s explanation of the need for infinite event space suggests it’s not very interesting.